Each week you must do a minimum of 18 hours of homework. Participation in sports requires at least 12 hours per week. You have no more than 35 hours per week in total to devote to these activities.
- Write a system of inequalities to model the situations.
How do you write it? Thanks
18 + 12 < 35 (?)
To write a system of inequalities to model the situations, we need to consider the constraints given in the problem.
Let's use the variables h and s to represent the number of hours spent on homework and sports, respectively.
The given constraints are:
1. Each week requires a minimum of 18 hours of homework:
h ≥ 18
2. Participation in sports requires at least 12 hours per week:
s ≥ 12
3. The total time available is no more than 35 hours per week:
h + s ≤ 35
Combining all these inequalities, our system of equations is:
h ≥ 18
s ≥ 12
h + s ≤ 35
Note that ≥ implies "greater than or equal to," and ≤ implies "less than or equal to."
To write a system of inequalities to model the situations given, we need to define variables and set up the inequalities accordingly.
Let's say we have two variables:
- Let x represent the number of hours spent on homework each week.
- Let y represent the number of hours spent on sports each week.
Now, let's consider the given conditions:
1. Each week, a minimum of 18 hours of homework must be done.
This can be represented as: x ≥ 18.
2. Participation in sports requires at least 12 hours per week.
This can be represented as: y ≥ 12.
3. The total time available per week for all activities is no more than 35 hours.
This can be represented as: x + y ≤ 35.
Combining these three inequalities gives us the complete system:
x ≥ 18
y ≥ 12
x + y ≤ 35
These inequalities model the given situation. Given any values for x and y that satisfy these conditions, you can determine whether the criteria are being met.